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A297273 Numbers whose base-11 digits have greater down-variation than up-variation; see Comments. 4
11, 22, 23, 33, 34, 35, 44, 45, 46, 47, 55, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 77, 78, 79, 80, 81, 82, 83, 88, 89, 90, 91, 92, 93, 94, 95, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 132, 143, 154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Suppose that n has base-b digits b(m), b(m-1), ..., b(0).  The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1).  The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b).  See the guide at A297330.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

154 in base-11:  1,3,0, having DV = 3, UV = 2, so that 154 is in the sequence.

MATHEMATICA

g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];

x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];

b = 11; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];

w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];

Take[Flatten[Position[w, -1]], 120]   (* A297273 *)

Take[Flatten[Position[w, 0]], 120]    (* A297274 *)

Take[Flatten[Position[w, 1]], 120]    (* A297275 *)

CROSSREFS

Cf. A297330, A297274, A297275.

Sequence in context: A048136 A180054 A166713 * A296746 A095779 A062055

Adjacent sequences:  A297270 A297271 A297272 * A297274 A297275 A297276

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 16 2018

STATUS

approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)